Problem: Simplify the following expression: $\sqrt{6} + \sqrt{24}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{6} + \sqrt{24}$ $= \sqrt{6} + \sqrt{4 \cdot 6}$ Separate the radicals and simplify. $= \sqrt{6} + \sqrt{4} \cdot \sqrt{6}$ $= \sqrt{6} + 2\sqrt{6}$ Finally, simplify by combining the terms. $= ( 1 + 2 )\sqrt{6} = 3\sqrt{6}$